Expand the Logarithmic Expression log base 4 of (y^2)/(16x)

$\log_{4} (\frac{y^{2}}{16 x})$

Rewrite $\log_{4} (\frac{y^{2}}{16 x})$ as $\log_{4} (y^{2}) - \log_{4} (16 x)$ .

$\log_{4} (y^{2}) - \log_{4} (16 x)$

Expand $\log_{4} (y^{2})$ by moving $2$ outside the logarithm.

$2 \log_{4} (y) - \log_{4} (16 x)$

Rewrite $\log_{4} (16 x)$ as $\log_{4} (16) + \log_{4} (x)$ .

$2 \log_{4} (y) - (\log_{4} (16) + \log_{4} (x))$

Logarithm base $4$ of $16$ is $2$ .

$2 \log_{4} (y) - (2 + \log_{4} (x))$

Simplify each term.

Apply the distributive property.

$2 \log_{4} (y) - 1 \cdot 2 - \log_{4} (x)$

Multiply $- 1$ by $2$ .

$2 \log_{4} (y) - 2 - \log_{4} (x)$